## Thursday, 22 September 2016

We were discussing various basic concepts of thermodynamics such as “Clausius theorem” in our recent post. We have also discussed “change in entropy for a reversible process and also for an irreversible process in thermodynamics in our previous post.

Today we will see here the concept of “Temperature entropy (T-S) diagram in thermal engineering with the help of this post.

### Temperature entropy (T-S) diagram

If we plot the absolute temperature over Y axis and entropy over X axis then we will secure one diagram and that diagram will be termed as temperature entropy diagram.

Following figure, displayed here, indicates the temperature entropy (T-S) diagram for water. Entropy will be shown over X-axis and temperature will be displayed over Y-axis as shown in figure.
Temperature entropy (T-S) diagram for water
We may see one very important point in temperature entropy diagram and that is critical point and usually written as CP. Critical point is also termed as critical state. Let us first try to understand the concept of critical point and after that we will see other features of temperature entropy diagram in this post.

Critical point will occur under conditions at which no phase boundaries exist. There will be multiple types of critical point such as liquid-liquid critical point or liquid vapour critical point.

As we can see in above figure that critical point connects two lines. Left line will be termed as saturated liquid line and right side line will be termed as saturated vapour line.

There will be three regions in the temperature entropy diagram. Liquid subcooled region, 2-phase region and the last one superheated vapour region and these regions are displayed here as shown in figure. 2-Phase region is also termed as mixture of vapour and liquid region.

Let us consider two point A and B. Point A is on liquid saturated line and point B is on saturated vapour line. AB line will be an isothermal line and isobaric line also and therefore we have assumed the temperature TA and pressure PA for point A and point B as shown in above figure.

Let we have considered an infinitesimal element ab of thickens dS for the process PQ as shown in above figure. dQ heat is received by the working fluid in an elementary section ab during the process PQ. Temperature could be assumed constant for this elementary section ab.

Area below the curve will provide the value of heat energy added to the working fluid in an elementary section ab.
Therefore, we will have
dQ = T. dS
If we want to determine the heat energy added to the working fluid during the process PQ, we will have following equation.
We will see another topic i.e. "Principle of increase of entropy" in our next post in the category of thermal engineering.
Do you have suggestions? Please write in comment box

### Reference:

Engineering thermodynamics by P.K. Nag